You are given two jugs, a 4-gallon one and a 3-gallon one. Neither has any measuring marker on it. There is a tap that can be used to fill the jugs with water. How can you get exactly 2 gallons of water into the 4-gallon jug?
Use Depth -First search but after the initial {0,0} state, continue your search from the {0,3} successor instead of the {4,0} successor.